bchdeco.m

数字通信第四版原书的例程

function [msg, err, ccode] = bchdeco(code, k, t, ord);
%BCHDECO Decodes a codeword using BCH decode method.
%       MSG = BCHDECO(CODE, K, T) recovers a message signal MSG from a
%       codeword CODE using BCH code technique provided K is the message
%       length and T is the error-correction capability.
%
%       MSG = BCHDECO(CODE, K, T, ORD) specifies the primitive polynomial in
%       producing the minimal polynomial of the BCH code.
%
%       [MSG, ERR] = BCHDECO(...) outputs the corrected error number. When 
%       the number of errors is larger than t, the error correction
%       capability, ERR equals -1.
%
%       [MSG, ERR, CCODE] = BCHDECO(...) outputs corrected codeword.
%
%       This example uses BCHDECO to process a three error correction code.
%       [pg, pm, cs, h, t] = bchpoly(15, 5);  % produce generator polynomial
%       [h, gen] = cyclgen(15, pg);           % produce generator matrix
%       msg = randint(100, 5);                % message signal
%       code = encode(msg, gen);              % encode
%       code = rem(code + randbit(100,15,[.3,.3,.3]), 2);   % add errors.
%       [dec, err] = bchdeco(code, 5, t);     % decode

%       Wes Wang 8/3/94, 9/30/95
%       Copyright (c) 1995-96 by The MathWorks, Inc.
%       $Revision: 1.1 $  $Date: 1996/04/01 17:52:03 $
%

% The algorithm used in this function is provided in Shu Lin's book.
% This function process binary BCH decoding.

%routine check
if nargin < 3
    error('Not enough input variable for BCHDECO');
end;

% assign initial parameter, further parameter check.
[n_code, m_code] = size(code);

% the dimension of the primitive polynomial in generating the BCH minimal polynomial
dim = 3;
pow_dim = 2^dim -1;
while pow_dim < m_code
    dim = dim + 1;
    pow_dim = 2^dim - 1;
end;

% In case of specified primitive polynomial
if nargin > 3
    ord = ord(:)';
    n_ord = length(ord);
    
    % it should be a vector.
    if n_ord ~= pow_dim - k + 1
        error(['The primitive polynomial ORD must have order ', num2str(dim)])
    end;

    % the primitive polynomial must be binary
    if ~isempty([find(floor(ord) ~= ord) find(ord < 0) find(ord > 1)])
        error('The primitive polynomial ORD has illegal coeficients');
    end;
%    [ord, rm] = gfdeconv([1, zeros(1, pow_dim-1), 1], ord);
    ord = gfprimdf(dim);
else
    % provide the default primitive polynomial
    ord = gfprimdf(dim);
end;
    
if (pow_dim ~= m_code)
    % the dimension of the code word and the parity-check matrix do not match
    error('The dimension of the code word and the parity-check matrix do not match');
end;

% the complete list of all element in GF(2^dim)    
tp = gftuple([-1:pow_dim-1]', ord);

% there is no error at the very begining
err = zeros(n_code,1);

% compute each code word in the transfer
for n_i = 1 : n_code
    [msg(n_i,:), err(n_i), ccode(n_i, :)] = ...
        bchcore(code(n_i,:), pow_dim, dim, k, t, tp);
end;

%--end of bchdeco--